Such a dual wet clutch with single clutches, which are axially arranged one behind the other and are (or can be) hydraulically actuated, is known from German Patent No. 38 19 702 (Rispeter et al.), whereby the hydraulic actuation devices are arranged axially in front of and behind the individual clutches and with the same diameter as the single clutches. The axial space required for this dual wet clutch is therefore comparatively large. In order to decrease the axial space required, the hydraulic actuation devices can be shifted radially inwards and arranged to axially overlap the individual clutches if necessary, as known from United Kingdom Patent Application No. 2 191 252, (Arrowsmith et al.), German Patent No. 9 114 528, (Zahnradfabrik Friedrichshafen AG), German Patent No. 38 38 865 (Friedmann), German Patent No. 2 116 311 (Brendecke) and German Patent No. 35 27 399 (Klaue). An even more compact design can be achieved using a common coupling web firmly connected with the clutch housing between both single clutches and both cylinder/piston pairs, as is known from U.S. Pat. No. 3,424,033 (Croswhite) or European Patent No. 1 195 537(Hegerath). However, the construction of this common element known from both of these publications causes crosstalk between the individual clutches due to the joint support of the engagement force via the coupling web.